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# Analytical Solution Methods for Boundary Value Problems

• Author : A.S. Yakimov
• Release : 13 August 2016
• ISBN : 0128043636
• Pages : 200 pages
• Rating : 4/5 from 21 ratings

Summary:
Analytical Solution Methods for Boundary Value Problems is an extensively revised, new English language edition of the original 2011 Russian language work, which provides deep analysis methods and exact solutions for mathematical physicists seeking to model germane linear and nonlinear boundary problems. Current analytical solutions of equations within mathematical physics fail completely to meet boundary conditions of the second and third kind, and are wholly obtained by the defunct theory of series. These solutions are also obtained for linear partial differential equations of the second order. They do not apply to solutions of partial differential equations of the first order and they are incapable of solving nonlinear boundary value problems. Analytical Solution Methods for Boundary Value Problems attempts to resolve this issue, using quasi-linearization methods, operational calculus and spatial variable splitting to identify the exact and approximate analytical solutions of three-dimensional non-linear partial differential equations of the first and second order. The work does so uniquely using all analytical formulas for solving equations of mathematical physics without using the theory of series. Within this work, pertinent solutions of linear and nonlinear boundary problems are stated. On the basis of quasi-linearization, operational calculation and splitting on spatial variables, the exact and approached analytical solutions of the equations are obtained in private derivatives of the first and second order. Conditions of unequivocal resolvability of a nonlinear boundary problem are found and the estimation of speed of convergence of iterative process is given. On an example of trial functions results of comparison of the analytical solution are given which have been obtained on suggested mathematical technology, with the exact solution of boundary problems and with the numerical solutions on well-known methods. Discusses the theory and analytical methods for many differential equations appropriate for applied and computational mechanics researchers Addresses pertinent boundary problems in mathematical physics achieved without using the theory of series Includes results that can be used to address nonlinear equations in heat conductivity for the solution of conjugate heat transfer problems and the equations of telegraph and nonlinear transport equation Covers select method solutions for applied mathematicians interested in transport equations methods and thermal protection studies Features extensive revisions from the Russian original, with 115+ new pages of new textual content

## Analytical Solution Methods for Boundary Value Problems

• Author : A.S. Yakimov
• Release : 13 August 2016

Analytical Solution Methods for Boundary Value Problems is an extensively revised, new English language edition of the original 2011 Russian language work, which provides deep analysis methods and exact solutions for mathematical physicists seeking to model germane linear and nonlinear boundary problems. Current analytical solutions of equations within mathematical physics fail completely to meet boundary conditions of the second and third kind, and are wholly obtained by the defunct theory of series. These solutions are also obtained for linear partial differential

## Boundary Value Problems for Analytic Functions

• Author : Jian-Ke Lu
• Publisher : World Scientific
• Release : 04 February 1994

Readership: Mathematicians. keywords:Cauchy Type Integral;Riemann Boundary Value Problem;Hilbert Boundary Value Problem;Index;Singular Integral Equation;Plemelj Formula;Characteristic Function;Standard Function;Noethor Theorem;Extended Residue Theorem “The book is self-contained and clearly written … It can well be used for advanced courses in complex analysis and for seminars, and is readable by graduate students themselves.” Mathematics Abstracts

## Numerical-Analytic Methods in the Theory of Boundary-Value Problems

• Author : M Ronto,A M Samoilenko
• Publisher : World Scientific
• Release : 30 June 2000

This book contains the main results of the authors' investigations on the development and application of numerical-analytic methods for ordinary nonlinear boundary value problems (BVPs). The methods under consideration provide an opportunity to solve the two important problems of the BVP theory — namely, to establish existence theorems and to build approximation solutions. They can be used to investigate a wide variety of BVPs. The Appendix, written in collaboration with S I Trofimchuk, discusses the connection of the new method with

## Analytical Solutions for Two Ferromagnetic Nanoparticles Immersed in a Magnetic Field

• Author : Gehan Anthonys
• Publisher : Morgan & Claypool Publishers
• Release : 01 February 2018

The investigation of the behavior of ferromagnetic particles in an external magnetic field is important for use in a wide range of applications in magnetostatics problems, from biomedicine to engineering. To the best of the author's knowledge, the systematic analysis for this kind of investigation is not available in the current literature. Therefore, this book contributes a complete solution for investigating the behavior of two ferromagnetic spherical particles, immersed in a uniform magnetic field, by obtaining exact mathematical models on

## Numerical-analytic Methods in the Theory of Boundary-value Problems

• Author : Nikola? Iosifovich Ronto,Anatoli? Mikha?lovich Samo?lenko
• Publisher : World Scientific
• Release : 17 May 2022

This book contains the main results of the authors' investigations on the development and application of numerical-analytic methods for ordinary nonlinear boundary value problems (BVPs). The methods under consideration provide an opportunity to solve the two important problems of the BVP theory ? namely, to establish existence theorems and to build approximation solutions. They can be used to investigate a wide variety of BVPs.The Appendix, written in collaboration with S I Trofimchuk, discusses the connection of the new method with

## Constructive Methods for Linear and Nonlinear Boundary Value Problems for Analytic Functions

• Author : v Mityushev,S V Rogosin
• Publisher : CRC Press
• Release : 29 November 1999

Constructive methods developed in the framework of analytic functions effectively extend the use of mathematical constructions, both within different branches of mathematics and to other disciplines. This monograph presents some constructive methods-based primarily on original techniques-for boundary value problems, both linear and nonlinear. From among the many applications to which these methods can apply, the authors focus on interesting problems associated with composite materials with a finite number of inclusions. How far can one go in the solutions of problems

Book Constructive Methods for Linear and Nonlinear Boundary Value Problems for Analytic Functions PDF Download/ Read Online

## Analogues for the Solution of Boundary-Value Problems

• Author : B. A. Volynskii,V. Ye. Bukhman
• Publisher : Elsevier
• Release : 17 May 2014

Analogues for the Solution of Boundary-Value Problems considers the simulation of integral methods of solving boundary-value problems. This book is organized into 11 chapters. After the introduction provided in Chapter I, the formulation of some important engineering problems that reduce to the solution of partial differential equations is reviewed in Chapter II. Chapter III covers the mathematical methods for the solution of problems, such as the thermal problem of electrode graphitization and underground coal gasification. The theory of the physical processes

## Boundary Value Problems for Engineers

• Author : Ali Ümit Keskin
• Publisher : Springer
• Release : 19 June 2019

This book is designed to supplement standard texts and teaching material in the areas of differential equations in engineering such as in Electrical ,Mechanical and Biomedical engineering. Emphasis is placed on the Boundary Value Problems that are often met in these fields.This keeps the the spectrum of the book rather focussed .The book has basically emerged from the need in the authors lectures on “Advanced Numerical Methods in Biomedical Engineering” at Yeditepe University and it is aimed to assist

## Modeling and Analysis of Chemical Engineering Processes

• Author : K. Balu,K. Padmanabhan
• Publisher : I. K. International Pvt Ltd
• Release : 01 January 2007

The chemical process industry faces serious problems with regard to new materials and efficient methods of production due to increasing costs of energy, stringent environmental regulations and global competition. A clear understanding of the processes is required in order to solve these problems. One way is through crisp modeling method; another is through an optimal operation of the process to improve profitability and efficiency. The book is in two parts. The first part discusses the methods of modeling chemical engineering

## Boundary Value Problems of Heat Conduction

• Author : M. Necati Ozisik
• Publisher : Courier Corporation
• Release : 26 November 2013

Intended for first-year graduate courses in heat transfer, this volume includes topics relevant to chemical and nuclear engineering and aerospace engineering. The systematic and comprehensive treatment employs modern mathematical methods of solving problems in heat conduction and diffusion. Starting with precise coverage of heat flux as a vector, derivation of the conduction equations, integral-transform technique, and coordinate transformations, the text advances to problem characteristics peculiar to Cartesian, cylindrical, and spherical coordinates; application of Duhamel's method; solution of heat-conduction problems; and

## Unified Transform for Boundary Value Problems

• Author : Athanasios S. Fokas,Beatrice Pelloni
• Publisher : SIAM
• Release : 30 December 2014

This book describes state-of-the-art advances and applications of the unified transform and its relation to the boundary element method. The authors present the solution of boundary value problems from several different perspectives, in particular the type of problems modeled by partial differential equations (PDEs). They discuss recent applications of the unified transform to the analysis and numerical modeling of boundary value problems for linear and integrable nonlinear PDEs and the closely related boundary element method, a well-established numerical approach for

## Partial Differential Equations

• Author : R. M. M. Mattheij,S. W. Rienstra,J. H. M. ten Thije Boonkkamp
• Publisher : SIAM
• Release : 01 January 2005

Partial differential equations (PDEs) are used to describe a large variety of physical phenomena, from fluid flow to electromagnetic fields, and are indispensable to such disparate fields as aircraft simulation and computer graphics. While most existing texts on PDEs deal with either analytical or numerical aspects of PDEs, this innovative and comprehensive textbook features a unique approach that integrates analysis and numerical solution methods and includes a third component - modeling - to address real-life problems. The authors believe that